diff --git a/util/include/istd_util/tile_geometry.h b/util/include/istd_util/tile_geometry.h
index 17794de..5f9c6e6 100644
--- a/util/include/istd_util/tile_geometry.h
+++ b/util/include/istd_util/tile_geometry.h
@@ -2,9 +2,9 @@
 #define ISTD_UTIL_TILE_GEOMETRY_H
 
 #include "istd_util/vec2.h"
+#include <array>
 #include <cstdint>
 #include <generator>
-#include <tuple>
 
 namespace istd {
 
@@ -24,10 +24,30 @@ namespace istd {
  * @return Generator yielding (i, j) tuples for each tile crossed by the
  * segment.
  */
-std::generator<std::tuple<std::int32_t, std::int32_t>> tiles_on_segment(
+std::generator<std::array<std::int32_t, 2>> tiles_on_segment(
 	Vec2 p1, Vec2 p2
 ) noexcept;
 
+/**
+ * @brief Computes the first intersection point between a line segment and a
+ * tile in the tilemap.
+ *
+ * Uses a coordinate system where x points downward (row index) and y points
+ * rightward (column index). Finds the intersection point (closest to p1)
+ * between the segment from p1 to p2 and the square tile specified by (i, j),
+ * where the tile is defined as the region from (i, j) to (i+1, j+1).
+ *
+ * @param p1 The starting point of the segment (floating point coordinates).
+ * @param p2 The ending point of the segment (floating point coordinates).
+ * @param tile The tile indices (i, j) representing the square from (i, j) to
+ * (i+1, j+1).
+ * @return The intersection point as a Vec2, or an undefined value if there is
+ * no intersection.
+ */
+Vec2 tile_segment_intersection(
+	Vec2 p1, Vec2 p2, std::array<std::int32_t, 2> tile
+) noexcept;
+
 } // namespace istd
 
 #endif
\ No newline at end of file
diff --git a/util/src/tile_geometry.cpp b/util/src/tile_geometry.cpp
index 4a04c0c..78b2b63 100644
--- a/util/src/tile_geometry.cpp
+++ b/util/src/tile_geometry.cpp
@@ -3,7 +3,7 @@
 namespace istd {
 
 // Amanatides-Woo Algorithm
-std::generator<std::tuple<std::int32_t, std::int32_t>> tiles_on_segment(
+std::generator<std::array<std::int32_t, 2>> tiles_on_segment(
 	Vec2 p1, Vec2 p2
 ) noexcept {
 	auto [i, j] = p1.floor();
@@ -38,7 +38,13 @@ std::generator<std::tuple<std::int32_t, std::int32_t>> tiles_on_segment(
 
 	auto [end_i, end_j] = p2.floor();
 	while (i != end_i || j != end_j) {
-		if (t_max.x < t_max.y) {
+		if (std::abs(t_max.x - t_max.y) < 1e-6f) {
+			// Both directions are equal, choose one arbitrarily
+			i += step_x;
+			j += step_y;
+			t_max.x += t_delta.x;
+			t_max.y += t_delta.y;
+		} else if (t_max.x < t_max.y) {
 			i += step_x;
 			t_max.x += t_delta.x;
 		} else {
@@ -49,4 +55,48 @@ std::generator<std::tuple<std::int32_t, std::int32_t>> tiles_on_segment(
 	}
 }
 
+Vec2 tile_segment_intersection(
+	Vec2 p1, Vec2 p2, std::array<std::int32_t, 2> tile
+) noexcept {
+	// Tile bounds: [i, i+1) x [j, j+1)
+	float i = static_cast<float>(tile[0]);
+	float j = static_cast<float>(tile[1]);
+	float min_x = i, max_x = i + 1;
+	float min_y = j, max_y = j + 1;
+
+	// Parametric line: p = p1 + t * (p2 - p1), t in [0, 1]
+	Vec2 d = p2 - p1;
+	float t_min = 0.0f, t_max = 1.0f;
+
+	// For each slab (x and y), compute intersection interval
+	for (int axis = 0; axis < 2; ++axis) {
+		float p = axis == 0 ? p1.x : p1.y;
+		float q = axis == 0 ? d.x : d.y;
+		float slab_min = axis == 0 ? min_x : min_y;
+		float slab_max = axis == 0 ? max_x : max_y;
+		if (std::abs(q) < 1e-8f) {
+			// Parallel to slab, outside
+			if (p < slab_min || p > slab_max) {
+				return Vec2::invalid();
+			}
+		} else {
+			float t1 = (slab_min - p) / q;
+			float t2 = (slab_max - p) / q;
+			if (t1 > t2) {
+				std::swap(t1, t2);
+			}
+			t_min = std::max(t_min, t1);
+			t_max = std::min(t_max, t2);
+			if (t_min > t_max) {
+				return Vec2::invalid();
+			}
+		}
+	}
+	// Intersection exists in [t_min, t_max], want closest to p1 (t_min >= 0)
+	if (t_min < 0.0f || t_min > 1.0f) {
+		return Vec2::invalid();
+	}
+	return p1 + d * t_min;
+}
+
 } // namespace istd
diff --git a/util/test/test_tile_geometry.cpp b/util/test/test_tile_geometry.cpp
index f77a20b..b6066c7 100644
--- a/util/test/test_tile_geometry.cpp
+++ b/util/test/test_tile_geometry.cpp
@@ -56,5 +56,43 @@ int main() {
 	assert(result.size() == 1);
 	assert(result[0] == std::make_tuple(7, 8));
 
+	// Test tile_segment_intersection: horizontal segment
+	p1 = Vec2(0.5f, 1.2f);
+	p2 = Vec2(0.5f, 4.8f);
+	{
+		Vec2 inter = tile_segment_intersection(p1, p2, {0, 2});
+		assert(inter.is_valid());
+		assert(std::abs(inter.x - 0.5f) < 1e-6);
+		assert(inter.y >= 2.0f && inter.y <= 3.0f);
+	}
+
+	// Test tile_segment_intersection: diagonal segment
+	p1 = Vec2(1.1f, 1.1f);
+	p2 = Vec2(3.9f, 3.9f);
+	{
+		Vec2 inter = tile_segment_intersection(p1, p2, {2, 2});
+		assert(inter.is_valid());
+		assert(inter.x >= 2.0f && inter.x <= 3.0f);
+		assert(inter.y >= 2.0f && inter.y <= 3.0f);
+	}
+
+	// Test tile_segment_intersection: no intersection
+	p1 = Vec2(0.0f, 0.0f);
+	p2 = Vec2(0.5f, 0.5f);
+	{
+		Vec2 inter = tile_segment_intersection(p1, p2, {2, 2});
+		assert(!inter.is_valid());
+	}
+
+	// Test tile_segment_intersection: segment starts inside tile
+	p1 = Vec2(2.2f, 2.2f);
+	p2 = Vec2(5.0f, 5.0f);
+	{
+		Vec2 inter = tile_segment_intersection(p1, p2, {2, 2});
+		assert(inter.is_valid());
+		assert(std::abs(inter.x - 2.2f) < 1e-6);
+		assert(std::abs(inter.y - 2.2f) < 1e-6);
+	}
+
 	return 0;
 }
diff --git a/util/test/test_vec2.cpp b/util/test/test_vec2.cpp
index 96cbebf..54deca4 100644
--- a/util/test/test_vec2.cpp
+++ b/util/test/test_vec2.cpp
@@ -1,5 +1,6 @@
 #include "istd_util/vec2.h"
 #include <cassert>
+#include <cmath>
 using namespace istd;
 
 int main() {